Answer:
[tex]y = 0.42x+55[/tex]
Step-by-step explanation:
Given
Let:
[tex]x \to miles[/tex]
[tex]y \to amount[/tex]
[tex](x_1,y_1) = (138,112.96)[/tex] ---- Bobs'
[tex](x_2,y_2) = (209,142.78)[/tex] --- Carl
Required
The equation
First, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{142.78 - 112.96}{209 - 138}[/tex]
[tex]m = \frac{29.82}{71}[/tex]
[tex]m = 0.42[/tex]
The equation is calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = 0.42(x - 138) + 112.96[/tex]
[tex]y = 0.42x - 57.96 + 112.96[/tex]
[tex]y = 0.42x+55[/tex]
Write ten rational numbers between 3/5 and 3/4
Answer:
Any of these numbers will work:
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.70
0.71
0.72
0.73
0.74
3/5 is .60
3/4 is .75
These are all rational numbers that fall within those two numbers.
Which expression is equivalent to -6(3x - 2/3)?
-6(3x-2/3)
=(-6).3x-(-6).2/3
=-18x-(-4)
=-18x+4
Lance is selling T-shirts for $10 each and hats for $12.50 each. He wants to earn at least $400 per week to cover his expenses. Which graph best represents the number of T-shirts and hats Lance should sell to meet his goal?
Answer:
Step-by-step explanation:
Jim is the quarterback on his football team.
He was sacked 3 times during the game.
Each time he was sacked, the team lost 7
yards. What was the total number of yards
lost from the sacks?
Answer: 21 yards
Step-by-step explanation:
Multiply 3 by 7 to find the number of years lost from the sacks because he was sacked 3 times and each time he lost 7 yards.
He lost 7 yards per sack , so in three sacks he will lose 21 yards.
3* 7 = 21
the second difference 4;x;8;y;20;.... is 2
9514 1404 393
Answer:
x = 5y = 13Step-by-step explanation:
First differences are ...
x -4, 8 -x, y -8, 20 -y
Then second differences are ...
(8 -x) -(x -4)
(y -8) -(8 -x)
(20 -y) -(y -8)
Each of these is said to be 2, so we have ...
12 -2x = 2 ⇒ x = 5
28 -2y = 2 ⇒ y = 13
And an equation we can use to check:
x +y -16 = 2 ⇒ 5 +13 -16 = 2 . . . . true
_____
The explicit formula for the sequence is ...
an = n^2 -2n +5
Find the value of x if x/3-2=6
Step-by-step explanation:
hope it is helpful to you
stay safe happy and healthy
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{\dfrac{x}{3}-2=6}[/tex]
[tex]\mathsf{= \dfrac{1}{3}x - 2 = 6}[/tex]
[tex]\textsf{ADD 2 BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{1}{3}x - 2 + 2 = 6 + 2}[/tex]
[tex]\textsf{CANCEL out: -2 + 2 because that gives you 1}[/tex]
[tex]\textsf{KEEP: 6 + 2 because that helps solve for x}[/tex]
[tex]\mathsf{6 + 2 = \boxed{\bf 8}}[/tex]
[tex]\mathsf{NEW \ EQUATION: \dfrac{1}{3}x = 8}[/tex]
[tex]\textsf{MULTIPLY 8 to BOTH SIDES}[/tex]
[tex]\mathsf{3\times\dfrac{1}{3}x=3\times8}[/tex]
[tex]\mathsf{CANCEL\ out: \ 3 \times \dfrac{1}{3} \ because \ that \ gives \ you \ 1}[/tex]
[tex]\mathsf{KEEP: \ 3 \times 8 \ because \ that\ gives \ you \ the \ value \ of \ x}[/tex]
[tex]\mathsf{\boxed{\bf x}= 3\times8}[/tex]
[tex]\mathsf{3\times8 = \boxed{\bf x}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf x = 24}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Five children have to form a queue. In how many different ways can they be arranged?
A. 120
B. 100
C. 60
D. 80
Answer:
120 different ways
The total number of ways to do this is the product because of the fundamental counting principle[1]. So 5x4x3x2x1 = 5! (read as “5 factorial”[2]) = 120 different ways to line up those 5 people. Five people lining up essentially means 5 people sorting into 5 positions.
1
2
3
VX
Which is a unit rate?
4 dollars
3 cans
5 students
2 teachers
6 hours 1 book
O 3 mies 2 days
Answer:
6 hours to 1 book
Step-by-step explanation:
Which is a unit rate?
4 dollars to 3 cans
5 students to 2 teachers
6 hours to 1 book
3 miles to 2 days
A unit rate is a rate of a number to 1. The second number must be 1. The only unit rate is 6 hours to 1 book.
Answer: 6 hours to 1 book
The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5
Answer:
4.7
Step-by-step explanation:
the median is the middle number in a set of numbers so first we need to put them in order
1.9 3.4 [4.7] 6.5 7.6
this one is easy since we have an odd number of digits
the answer is 4.7
Which of the following inequalities represents all values of X for which the quotient below is defined?
Answer:
[tex]x \ge 1[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{6(x - 1)} \div \sqrt{3x^2[/tex]
Required
x for [tex]which[/tex] the function is [tex]de fi ned[/tex]
To do this, we set the numerator root [tex]\ge 0[/tex]
So, we have:
[tex]6(x - 1) \ge 0[/tex]
Divide by 6
[tex](x - 1) \ge 0[/tex]
Solve for x
[tex]x \ge 1[/tex]
Also, we set the denominator greater than 0:
[tex]3x^2 > 0[/tex]
Divide by 3
[tex]x^2 > 0[/tex]
Take square roots
[tex]x > 0[/tex]
So, we have:
[tex]x > 0[/tex] and [tex]x \ge 1[/tex]
Combine both to give:
[tex]x \ge 1[/tex]
PLEASE HELP!! I WILL GIVE BRAINLIEST AND POINTS!!
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
f(x) = -x2 - 6x
Answer:
Rewrite in vertex form and use this form to find the vertex
Rewrite in vertex form and use this form to find the vertex
(h,k).(−3,9)
Step-by-step explanation:
Enter the correct answer in the box.
if x ≠0 what is the sum of 4 ^3/ x^10 + 5 3 ^3/8x in simplest form? Ignore the answer that’s already there
9514 1404 393
Answer:
14x³∛x
Step-by-step explanation:
Factor cubes from under the radical and combine like terms.
[tex]\displaystyle 4\sqrt[3]{x^{10}}+5x^3\sqrt[3]{8x}=4\sqrt[3]{x(x^3)^3}+5x^3\sqrt[3]{x(2^3)}\\\\=4x^3\sqrt[3]{x}+5x^3\cdot2\sqrt[3]{x}=(4+5\cdot2)x^3\sqrt[3]{x}\\\\=\boxed{14x^3\sqrt[3]{x}}[/tex]
_____
Additional comment
When using an equation editor to create your answers, you need to be careful to make the distinction between the multiplication symbol × and the variable x. Note, too, that exponents generally must be written using the superscript form. x10 and x¹⁰ are not the same thing.
HELPPPPPPPPPP
Which of the following is equivalent to the expression below ?
square root 8 minus square root 72 plus square root 50 ?
A. 13 square root 2
B. 7 square root 2
C. 3 square root 2
D. Square root 2
Answer:
a13 square root
..cv
..
..
A student measured the lead content of a paint sample 4 times. The standard deviation of the measurements was found to be 0.76% of the average. Calculate the confidence interval at the 90% confidence level.
Answer:
[tex]CI =0.894%[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=4[/tex]
Standard deviation [tex]\sigma=0.76\% of \=x[/tex]
Confidence level [tex]\mu =90\%=0.90[/tex]
Degree of Freedom [tex]Df=n-1=3[/tex]
Therefore
Test T from table is given
[tex]t=2.353[/tex]
Generally the equation for Confidence interval CI is mathematically given by
[tex]CI =t*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]CI =2.353*\frac{0.76}{\sqrt{4}}[/tex]
[tex]CI =0.894%[/tex]
Someone help please!!
Answer:
9 (a) [tex]d = \frac{\sqrt{e}}{\sqrt{3}}[/tex]
9 (b) [tex]d = \frac{\sqrt{7k}}{\sqrt{2}}[/tex]
Step-by-step explanation:
Hope this helped!
Which statement is true about the function f(x)= sqrt of x?
If AABC= A DEF, which congruences are true by CPCTC? Check all that
apply.
APEC correct answer is:
AB =DE
AC= DF
See photo.
Answer:
Options A, B and D
Step-by-step explanation:
If the two triangles are congruent, their corresponding parts will be congruent.
If ΔABC ≅ ΔDEF
By the property of CPCTC,
AB ≅ DE
AC ≅ DF
BC ≅ EF
∠A ≅ ∠D
∠C ≅ ∠F
∠B ≅ ∠E
Therefore, Options A, B and D are the correct options.
You survey 300 students at the highschool. Of the 300 students, 103 of them said that pizza is their
favorite food. If 751 students attend the high school, about how many students would choose pizza as
their favorite food?
Answer:
258
Step-by-step explanation:
PLEASE ANSWER MAKE SURE YOU ARE RIGHT PLEASE I WILL MARK AS BRAINIEST
FIND THE VOLUME OF THE CYLINDER
Answer:
Find the volume of the cone, the answer i got was 37.68 but it asked to round so it should be 37.7
Hope this helps :)
Answer:
If we want to find volume of cone we must use this formule: πr²*high/3.
Step-by-step explanation:
let's solve step by step
firstly you know the radius is 3 and high is 4
if we accept π to 3. the answer is must be (3*3*4)/3 and finally the answer is 12 units³
(6) Milan added 3 fish to his pond each day for 27 days. What was the total change in the number
of fish in the pond?
fish
Answer: 81
Step-by-step explanation: 27 times 3 = 81
Answer: 81
Step-by-step explanation: 21 times 3
Complete the following statement mentally.
Answer:
The answer to your question is given below.
Step-by-step explanation:
Let the total number be U.
From the question given above, we were told that any number of B is 50% of the total number (i.e U).
Now, we shall determine the the total number (U) in terms of B.
50% of U = B
50/100 × U = B
50U / 100 = B
Cross multiply
50U = 100B
Divide both side by 50
U = 100B/50
U = 2B
Thus, the total number is 2B
Finally, we shall determine the answer to the question:
111 is 50% of ___
B = 111
Total number (U) = 2B
Total number (U) = 2 × 111
Total number (U) = 222
Therefore,
111 is 50% of 222
According to this diagram, what is tan 74°?
74°
25
7
16
90°
24
O A.
7
24
B. 24
C.
D. 24
O E. 25
F.
Option B is correct, the value of tan 74° is 24/7
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We have to find the value of tan74°
The tan function is ratio of opposite side and adjacent side.
We have to find the opposite side of angle 74°,
The opposite side has length 24
Now let us find the adjacent side of angle 74 which is 7
tan 74° = 24/7
Hence, option B is correct, the value of tan 74° is 24/7.
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Graph the image of trapezoid PQRS after a translation 9 units right and 10 units up.
These box plots show daily low temperature for a sample of days in two different towns
Answer:
The interquartile range (IQR) for town A, 15° is less than the IQR for town B, 20°.
Step-by-step explanation:
From the boxplot Given ;
Town A :
The first quartile, Q1 = 15
Third quartile, Q3 = 30
The interquartile range, IQR = Q3 - Q1 = 30 - 15 = 15°
TOWN B :
The first quartile, Q1 = 20
Third quartile, Q3 = 40
The interquartile range, IQR = Q3 - Q1 = 40 - 20 = 20°
The interquartile range (IQR) for town A, 15° is less than the IQR for town B, 20°.
A sample of students at a university took a test that diagnosed their learning styles as active or reflective and also as visual or verbal. Each student received a numerical score on the active/reflective style and also a numerical score on the visual/verbal style. The sample size was 39, and the sample correlation coefficient turned out to equal .273.a. State the hypotheses for testing whether there is a positive correlation between these variables in the population of all students at this university.b. Calculate the value of the test statistic.c. Determine the p-value as accurately as possible.d. State the test decision for the α= .10 and α= .05 significance levels, and summarize your conclusion in context.e. If the sample size was much larger, and the value of the sample correlation coefficient stayed the same, describe the impact on your test statistic, p-value, and conclusion.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Sample size, n = 39
Correlation Coefficient, r = 0.273
The hypothesis test to examine if there is a positive correlation :
H0 : ρ = 0
If there is a positive correlation, then ρ greater than 1
H0 : ρ > 1
The test statistic :
T = r / √(1 - r²)/(n - 2)
T = 0.273 / √(1 - 0.273²)/(39 - 2)
T = 0.273 / 0.1581541
T = 1.726
The Pvalue using a Pvalue calculator can be be obtained using df = n - 2, df = 39 - 2 = 37
The Pvalue = 0.0463
α= .10 and α= .05
At α= .10
Pvalue < α ; Hence, we reject H0 and conclude that a positive correlation exists
At α= 0.05 ;
Pvalue < α ; Hence, we reject H0 and conclude that a positive correlation exists
The table shown gives values of the function y=g(x) for selected values of x.
Answer: C
Explanation:
A is eliminated because of 3 and 24, 3^2 is 9 and 9 times 3 isnt 24
B is eliminated because of 1 and 6, 2 plus 3 is 5 not 6
C works for all the number sets
D is eliminated because of 1 and 6, again 3 plus 2 is 5 not 6
The Punjab Highway department is studying traffic pattern on G.T. Road near Lahore. As part of previous study, population standard deviation is 680 number of vehicles per day. A random sample of 64 days gives mean of 5410 cars. Find a 90 percent confidence interval for population Mean (the average number of vehicles per day).
Answer:
for this we need 90 percent 5410
so we multiply 5410*0.9=4869
Hope This Helps!!!
Harold move no more than 43 of his sheep and goats into another field. fewer than 22 this animals are goats.
let s represent the number of sheep and let G represent the number of goats Identify two inequalities that represent this situation.
what is the answer?
(2a³b⁴)⁴=
Answer:
16a^12 b^16
Step-by-step explanation:
that's the answer. just multiply out the powers
Answer:
16*(a^12)*(b^16)
Step-by-step explanation:
In order to solve this problem, we can split these term into three separate terms.
[tex]{(2 {a}^{3} {b}^{4})}^{4} = {2}^{4} \times {( {a}^{3}) }^{4} \times {( {b}^{4} )}^{4} [/tex]
2 to the power of 4 is 16.
[tex] {2}^{4} = 16[/tex]
As for the terms a and b, the two exponents can multiply with each other.
[tex] {( {a}^{3} )}^{4} = {a}^{(3 \times 4)} = {a}^{12} [/tex]
[tex] {( {b}^{4} )}^{4} = {b}^{(4 \times 4)} = {b}^{16} [/tex]
Now, we can directly multiply the values together by combining into one term.
Hence, the final answer is
[tex]16 {a}^{12} {b}^{16} [/tex]
The relationship between the amounts of blue
and red paint needed to make a certain shade
of purple is shown in the following graph.
10+
9+
8+
7
6
Liters of red paint
5+
4+
3+
2
1
→
3
1
2
Liters of blue paint
Which statements about the graph are true?
Choose all answers that apply:
Answer:
B
Step-by-step explanation:
Had it on Khan Academy.
True statement for the given graph is the point [tex](3,9)[/tex] shows that [tex]9[/tex] liters of red paint are needed for every [tex]3[/tex] liters of blue paint.
What is graph?
" Graph is defined as diametrical representation of the relation between the variables on the coordinate plane along x-axis and y -axis."
According to the question,
As given in the graph,
Graph represents the linear relation between red paint and blue paint.
'x -axis' on the graph represents the blue paint
'y- axis' on the graph represents red paint
A. The point [tex](0,0)[/tex] shows that any amount of red and the blue paint will make same shade of purple.
From the graph coordinates [tex](1,3)[/tex] and [tex](2, 6)[/tex]represents that proportion of blue : red to make required purple shade is [tex]1: 3[/tex].
Hence, Option A is not a correct answer.
B. The point [tex](3,9)[/tex] shows that [tex]9[/tex] liters of red paint are needed for every [tex]3[/tex] liters of blue paint.
Coordinate [tex]( 3,9)[/tex] on the graph represents the ratio of blue : red [tex]= 3 : 9[/tex] which is equals to [tex]1:3[/tex] .
Hence, Option(B) is the correct answer.
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